Queensland Council for Civil Liberties vice-president Terry O'Gorman has likened the appointment to the Joh Bjelke-Petersen era selection of Terry Lewis who "leapfrogged" numerous senior officers to become police commissioner.

His condemnation comes a day after Peter Davis QC quit as head of the Queensland Bar Association, citing the leaking of confidential discussions he had with one of Attorney-General Jarrod Bleijie's senior staff about Mr Carmody's possible promotion.

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"The leaking of confidential discussions the attorney-general had with Peter Davis QC ... is an extraordinary development that cannot be left unaddressed," Mr O'Gorman said on Saturday in a statement.

Australian Bar Association president Mark Livesey QC is also questioning Mr Carmody's selection.

"The handling of this matter has seriously called into question the appointment process and judicial independence," he said.

In April, Mr Houghton wrote that Labor had nominated former Queensland solicitor-general Walter Sofronoff as the state's next chief justice.

Mr Sofronoff, who quit his post in March, has since called on Mr Carmody to decline his appointment, claiming he is too close to the government.

"He shouldn't be chief justice. He should do the gracious thing and realise that all of this has been a horrible mistake and say that he wouldn't accept the appointment," he told ABC television.

Mr Houghton's column also said Labor had nominated Court of Appeal president Margaret McMurdo as a possible chief justice.

An angry Ms Palaszcuk on Saturday insisted her correspondence in relation to the appointment process, which had been "provided to the attorney-general in confidence", had been leaked, and called for Mr Bleijie to resign.

"On Monday, the attorney-general should not be walking through the doors of this Executive Building," she told reporters outside the government's ministerial offices in Brisbane.

"The only reason he should go through these doors is to hand his resignation in to the premier of Queensland."

In a statement issued later on Saturday, a spokesman for Mr Bleijie said "nothing came from the attorney-general or his office".

However, he said Ms Palaszczuk had herself breached a confidentiality by publicly disclosing her recommendations for chief justice during a press conference on 7 May.

As chief magistrate in late 2013, Mr Carmody angered the legal profession by issuing a directive that all disputed bail applications made by alleged bikies be dealt with in one court room.

That meant he would, most likely, be presiding over the controversial cases.

Days after being appointed chief magistrate in September 2013, Mr Carmody and Mr Bleijie had a private dinner at the upmarket Urbane Restaurant in Brisbane, documents obtained by AAP show.

A spokesman for the attorney-general described that meeting as social catch-up.